As an important topic in hadron physics, the open-charm strong decays of
the charmonium states are often discussed in the literature [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}, [24]}, [25]}, [26]}.
Several pioneering works can be found in
Refs. [1]}, [2]}, [3]}, where the open charm strong decays of \(\psi (3770)\) ,
\(\psi (4040)\) , \(\psi (4160)\)  and \(\psi (4415)\)  have been evaluated about forty years ago.
Stimulated by first observed charmonium-like resonance \(X(3872)\)  at Belle [30]}
and CDF [31]}, Eichten, Lane and Quigg analyzed the open charm strong decays of charmonium
states near threshold in the Cornell coupled-channel model [4]}, [5]}.
In 2007, Ding, Zhu and Yan considered the open flavor strong decays of \(Y(4360)\)  and \(Y(4660)\)  as \(3 ^3D_1\)  and \(5 ^3S_1\) 
canonical charmonium in the simple harmonic oscillator wave function approximation in the framework of
flux tube model [6]}. In 2008, Segovia et al. calculated the open-flavor strong
decays of the \(J^{PC}=1^{--}\)  charmonium states in the \(^3P_0\)  model [7]},
where the new \(X(4360)\)  state was considered to be the \(\psi (4S)\)  state and the \(\psi (4415)\)  as
the \(\psi _1(3D)\)  state, which differs from other assignments. In 2009, as conventional charmonium states,
the open-flavor strong decays of the newly observed resonances \(X(3915)\)  and \(X(4350)\) 
were studied by Liu et al. within the \(^3P_0\)  model, the strong decay properties
indicate that they may be assigned as \(\chi _{c0}(2P)\)  and \(\chi _{c2}(3P)\) ,
respectively [24]}. Further studies of the open-flavor strong decays of
\(P\) -wave charmonium states were also carried out within the \(^3P_0\)  model by several groups
in recent years [8]}, [9]}, [11]}, [12]}. It is found that
\(X(3915)\)  may be disfavored the assignment of \(\chi _{c0}(2P)\)  [8]}, [9]},
the \(X(4140)\)  may favor the \(\chi _{c1}(3P)\)  state [11]}, while the newly observed state \(X^*(3860)\) 
can be a good candidate of \(\chi _{c0}(2P)\)  with a broad width [12]}.
Recently, the Bethe-Salpeter method was also extended to
deal with the open-charm strong decays of several charmonium states [13]}, [14]}, [15]}.
However, as emphasized earlier, systematic studies of the full spectrum are essential for a better understanding of the underlying dynamics. Furthermore, how to properly treat the strong \(S\) -wave threshold interactions is a key issue for the description of near-threshold states [48]}. The SP model can partially account for such an effect which makes the systematic comparison between the LP and SP model results interesting. Note that the most recent systematic study of the strong decays of higher charmonium
states was carried out by Barnes, Godfrey
and Swanson [22]} quite long ago. It is necessary to re-investigate in a systematic way
the strong decays of the higher charmonium states by combining the recent progress in theory
and experiments.
